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Simplifying 4y2 + -63y + -81 = 0 Reorder the terms: -81 + -63y + 4y2 = 0 Solving -81 + -63y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -20.25 + -15.75y + y2 = 0 Move the constant term to the right: Add '20.25' to each side of the equation. -20.25 + -15.75y + 20.25 + y2 = 0 + 20.25 Reorder the terms: -20.25 + 20.25 + -15.75y + y2 = 0 + 20.25 Combine like terms: -20.25 + 20.25 = 0.00 0.00 + -15.75y + y2 = 0 + 20.25 -15.75y + y2 = 0 + 20.25 Combine like terms: 0 + 20.25 = 20.25 -15.75y + y2 = 20.25 The y term is -15.75y. Take half its coefficient (-7.875). Square it (62.015625) and add it to both sides. Add '62.015625' to each side of the equation. -15.75y + 62.015625 + y2 = 20.25 + 62.015625 Reorder the terms: 62.015625 + -15.75y + y2 = 20.25 + 62.015625 Combine like terms: 20.25 + 62.015625 = 82.265625 62.015625 + -15.75y + y2 = 82.265625 Factor a perfect square on the left side: (y + -7.875)(y + -7.875) = 82.265625 Calculate the square root of the right side: 9.070039967 Break this problem into two subproblems by setting (y + -7.875) equal to 9.070039967 and -9.070039967.Subproblem 1
y + -7.875 = 9.070039967 Simplifying y + -7.875 = 9.070039967 Reorder the terms: -7.875 + y = 9.070039967 Solving -7.875 + y = 9.070039967 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.875' to each side of the equation. -7.875 + 7.875 + y = 9.070039967 + 7.875 Combine like terms: -7.875 + 7.875 = 0.000 0.000 + y = 9.070039967 + 7.875 y = 9.070039967 + 7.875 Combine like terms: 9.070039967 + 7.875 = 16.945039967 y = 16.945039967 Simplifying y = 16.945039967Subproblem 2
y + -7.875 = -9.070039967 Simplifying y + -7.875 = -9.070039967 Reorder the terms: -7.875 + y = -9.070039967 Solving -7.875 + y = -9.070039967 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.875' to each side of the equation. -7.875 + 7.875 + y = -9.070039967 + 7.875 Combine like terms: -7.875 + 7.875 = 0.000 0.000 + y = -9.070039967 + 7.875 y = -9.070039967 + 7.875 Combine like terms: -9.070039967 + 7.875 = -1.195039967 y = -1.195039967 Simplifying y = -1.195039967Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.945039967, -1.195039967}
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